Problem: Ben is 8 years older than Daniel. Two years ago, Ben was 5 times older than Daniel. How old is Ben now?
Explanation: We can use the given information to write down two equations that describe the ages of Ben and Daniel. Let Ben's current age be $b$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $b = d + 8$ Two years ago, Ben was $b - 2$ years old, and Daniel was $d - 2$ years old. The information in the second sentence can be expressed in the following equation: $b - 2 = 5(d - 2)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$ , we get: $d = b - 8$ . Substituting this into our second equation, we get the equation: $b - 2 = 5($ $(b - 8)$ $ -$ $ 2)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 2 = 5b - 50$ Solving for $b$ , we get: $4 b = 48$ $b = 12$.